5.1: Quadratic- involving the second and no higher power of an unknown quantity or variable: "a quadratic equation". Vertex- The highest point; the top or apex. X-intercept- The x-coordinate of the point where a line intersects the x-axis. Y-intercept- If the graph of an equation intersects the y-axis at the point (0,b) the number b is the y-intercept of the graph. Increasing- When the graph starts to increase. Decreasing-When the graph starts to decrease.
Maximum- Graph cant go any higher.
Minimum- Graph cant go any lower. Parabola-The set of all points equidistant from a point called the focus and a line called the directrix.
5.2: Summarize the similarities and differences between linear functions and quadratic functions. Discuss the graphs, the equations and the properties of each function. The linear function is y=mx+b, the quadratic function is ax squared +bx +c. Its almost the same because of the variables. When you graph a quadratic function it will be a "U" shape, when you graph a linear function it would be a straight line. In order to solve a quadratic function you have to plug it into the quadratic formula. In order to solve a linear function you have to plug 0 for y and 0 for x.
5.3: Joe is standing at the end zone of a football field and throws the football across the field. The function below models the path that football is thrown, in feet. f(x)=-2(x-75)squared +22
Answer the following questions in your wikispace.
What graphical shape did the football create as it flew through the air? upside down U shape.
Identify the vertex. (75,22)
Describe, in context, what the x-coordinate of the vertex represents. Is the distance down the field.
Describe, in context, what the y-coordinate of the vertex represents. Is the highest point.
Find f(2). Describe what your answer means in the context of the problem. f(2)= -10636. 2 feet down the field and -10636ft in the "air"
5.4: In your wiki space journal, describe the similarities and differences between the three graphs and equations. Be sure to compare the following features; y-intercept, x-intercepts, direction of the graph. Find the connection between these features and their equations - what causes them? They are all similar because they share a common U shape. Function 2 is different from function 1 and 3 because it opens down instead of up. When the first number or variable is a negative it opens down, and if it is a positive than it opens up. Function 1 and 3 x-values are both negative and y-values end up being positive. Function 2 x-values are positive and y-values end up being negative.
5.5: You and your friend are playing a game of tennis. Your friend throws the ball in the air, hitting the ball when it is 3 ft above the court with an initial velocity of 40 ft/sec. The height h(t) of the ball can be modeled by the function h(t) = -16t^2+40t+3, where t is the elapsed time in seconds after the dive.
Answer the following questions in your wikispace.
What shape does the path of the tennis ball make while traveling in the air. Upside down U shape.
Find h(1). Describe what h(1) means in the context of the problem. h(1)=27 In 1 second the ball is 27ft in the air.
What is the y-intercept of h(t). In context, what does the y-intercept represent? y-intercept is 3 which means the guy serves the ball once its 3ft up in the air.
Identify the vertex. Describe in context what the x-coordinate of the vertex represents. Describe in context what the y-coordinate of the vertex represents. (1.25,28) at 1.25 sec the ball reached its highest height of 28.
What is the x-intercept(s) of h(t). In context what does the x-intercept(s) represent? 0.078 and 2.42 they represents where the ball starts and where it ends.
5.6: In your own words, explain what the Zero Property Rule is and how and when it is used. Given the equation 0 = (2x-3)(x+5), verbally explain the step-by-step process to solve for x as you would to a brand new student entering our class.
You looked over at Joey's paper and noticed he had written 3 and -5 as his two solutions. Explain where Joey may have made his mistake? How would you prove to Joey that his solutions are not true?
5.7: In your wikispace, explain your thought process and order of matching the equations and graphs together.
What properties did you look at first? What types of equation did you match first? I separated them into 3 different groups of vertex forms intercept form and standard form and did vertex form first.
What type of equation was the hardest to match? Standard form because you have to factor them to get the x-intercepts.
How did you narrow down your choices? By figuring out the vertex,y-intercept,and x-intercept for each graph the divided the equations into 3 groups of vertex form,intercept form and standard form.
Vertex- The highest point; the top or apex.
X-intercept- The x-coordinate of the point where a line intersects the x-axis.
Y-intercept- If the graph of an equation intersects the y-axis at the point (0,b) the number b is the y-intercept of the graph.
Increasing- When the graph starts to increase.
Decreasing-When the graph starts to decrease.
Maximum- Graph cant go any higher.
Minimum- Graph cant go any lower.
Parabola-The set of all points equidistant from a point called the focus and a line called the directrix.
5.2: Summarize the similarities and differences between linear functions and quadratic functions. Discuss the graphs, the equations and the properties of each function. The linear function is y=mx+b, the quadratic function is ax squared +bx +c. Its almost the same because of the variables. When you graph a quadratic function it will be a "U" shape, when you graph a linear function it would be a straight line. In order to solve a quadratic function you have to plug it into the quadratic formula. In order to solve a linear function you have to plug 0 for y and 0 for x.
5.3:
Joe is standing at the end zone of a football field and throws the football across the field. The function below models the path that football is thrown, in feet. f(x)=-2(x-75)squared +22
Answer the following questions in your wikispace.
5.4: In your wiki space journal, describe the similarities and differences between the three graphs and equations. Be sure to compare the following features; y-intercept, x-intercepts, direction of the graph. Find the connection between these features and their equations - what causes them? They are all similar because they share a common U shape. Function 2 is different from function 1 and 3 because it opens down instead of up. When the first number or variable is a negative it opens down, and if it is a positive than it opens up. Function 1 and 3 x-values are both negative and y-values end up being positive. Function 2 x-values are positive and y-values end up being negative.
5.5: You and your friend are playing a game of tennis. Your friend throws the ball in the air, hitting the ball when it is 3 ft above the court with an initial velocity of 40 ft/sec. The height h(t) of the ball can be modeled by the function h(t) = -16t^2+40t+3, where t is the elapsed time in seconds after the dive.
Answer the following questions in your wikispace.
5.6: In your own words, explain what the Zero Property Rule is and how and when it is used. Given the equation 0 = (2x-3)(x+5), verbally explain the step-by-step process to solve for x as you would to a brand new student entering our class.
You looked over at Joey's paper and noticed he had written 3 and -5 as his two solutions. Explain where Joey may have made his mistake? How would you prove to Joey that his solutions are not true?
5.7:
In your wikispace, explain your thought process and order of matching the equations and graphs together.